The difference has to do with mismatch loss. The first, radiation efficiency, ignores antenna mismatch loss, and only looks at the power delivered to the antenna.

The second, total efficiency, is technically a function of the impedance of the radio and transmission line (typically 50 Ohms). Then the mismatch loss is calculated (see gamma, the reflection coefficient or
<a href="http://www.antenna-theory.com/definitions/vswr.php">VSWR</a>. The total efficiency can be increased with an impedance matching network, the radiation efficiency cannot.

If the antenna is exactly matched to the transmission line/radio, then
the two efficiencies are the same.